The optimal multi-copy Aloha

Multicopy Aloha is a generalization of single-copy Aloha where multiple copies of a packet are transmitted without first learning whether the transmission of the first copy is successful or not. Different users in the system can transmit different numbers of copies, but the optimal multicopy policy is found to be of the pure type whereby all users transmit the same number of copies. To maximize the probability of successful transmission it was found that the optimal copy number is one for the normalized channel traffic Λ in the range 0.48<Λ⩽1, two for 0.28<Λ⩽0.48, three for 0.20<Λ⩽0.28, etc. Potential applications of multicopy Aloha include packet satellite systems, multichannel Aloha systems, and reservation Aloha systems